第二章线性系统的数学描述(2)

1、自动控制原理杭州电子科技大学杭州电子科技大学“自动控制原理自动控制原理”精品课程课题组精品课程课题组2008.102006年度浙江省精品课程( )G s( )R s( )C s元件的结构图( )G s( )R s( )C s结构图的相加点(a)和分支点(b)(a)( ),( )u t U s ( ),( )r tR s( )( )u tr t( )( )U sR s+(b)( ),( )u t U s( ),( )u t U s小结小结：任何系统都可以由信号线、函数方块、信号：任何系统都可以由信号线、函数方块、信号引出点及求和点组成的方块图来表示。引出点及求和点组成的方块图来表示。max()s

2、sesrcsuKKEKaasuK u2212212211aaa aabmbbmm ammmdiuR iLEdtdEKdtMC iddJfMdtdtJJJifffi211cmiziz电位器电桥：电位器电桥：放大器：放大器：减速器减速器-齿轮系统齿轮系统(1)(1)列写各元件列写各元件的微分方程的微分方程(2)象方程象方程( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)

3、(sr )(sc )(se ( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us)(sr )(sc )(se ( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sr )(sc )(se sK)(sUs( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us)(se sK)(sUs( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )

4、( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ssaK)(sUs)(sUa)(sr )(sc )(se sK)(sUsaK)(sUa( )( )( )ercsss( )( )sseUsKs( )( )aasUsK Us( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmss

5、i( )( )bbmE sK ss)(sIamC)(sMm( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sMm)(sm sfJs 21( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sm sKb)(sEb( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC

6、Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss)(sm i1)(sc ( )( )( )( )aa aaabU sR I sL sI sE s( )( )mmaMsC Is2( )( )mmmJssfssM1( )( )cmssi( )( )bbmE sK ss闭环系统结构图（无干扰作用）( )G s( )H s( )R s( )E s( )C s( )B s+-( )( ) ( );C sG s E s( )( )( );E sR sB s( )( ) ( )BsH s C s( )( )( )( )B sG s H sE s( )( )( )

7、C sG sE s( )G s( )H s( )R s( )E s( )C s( )B s+-( )( ) ( )C sG s E s( )( )( )( )( ) ( )E sR sB sR sH s C s( )( )( )1( )( )C sG sR sG s H s( )G s( )H s( )R s( )E s( )C s( )B s+-( )( )( )1( )( )G sC sR sG s H s扰动作用下的闭环系统结构图1( )G s( )H s( )R s( )E s( )C s( )B s+-2( )G s扰动( )N s+212( )( )( )1( )( )( )NG

8、sCsN sG s G s H s1212( )( )( )( )1( )( )( )RG s G sCsR sG s G s H s2112( )( )( )( )( ) ( )( )1( )( )( )RNG sC sC sCsG s R sN sG S G s H s1( )G s( )H s( )R s( )E s( )C s( )B s+-2( )G s扰动( )N s+( )iG s1,2,in12( )( )( )( )nG sG s G sG s123( )( )( )G sG sG s0( )X s4( )X s(b)1( )G s2( )G s3( )G s0( )X s1

9、( )X s2( )X s3( )X s(a)4( )X s( )1( ) ( )G sG s H s( )R s( )C s(b)( )G s( )H s( )R s( )E s( )C s( )B s+ (a)( )( )( )( )1( )( )C sG sG sR sG s H s相加点前移(a) +( )G s( )R s( )Q s( )C s +( )G s( )R s( )C s( )Q s1( )G s(b)相加点后移 +( )G s( )R s( )C s( )Q s( )G s(b)(a) +( )G s( )R s( )Q s( )C s分支点前移(b)( )G s(

10、)R s( )C s( )G s( )C s(a)( )G s( )R s( )C s( )C s分支点后移1( )G s(b)( )G s( )R s( )C s( )R s(a)( )G s( )R s( )C s( )R s相邻相加点的移动ADCB +(a)DC +A +B(b)相邻分支点的移动AAAAA(a)AAAAA(b)G1G2G3G4H3H2H1abG1G2G3G4H3H2H1G41请你写出结果请你写出结果,行吗？行吗？错！错！G2H1G1G3G1G2G3H1G2无用功无用功向同类移动向同类移动G1G1G4H3G2G3H1H1H3G1G4G2G3H3H1引言信号流图12345xx

11、xxx1245xxxx125xxx232;xxx2432;xxxx343;xxx2532xxxx24532;xxxxx3453;xxxx44xx232xxx和44xx2532xxxx 和44xx1kkkPP(1)(2)(3)()1( 1)mmLLLL (1)L(2)L(3)L()mL某系统的结构图+1G1H3G2G2H( )R s( )C s1123PGG G1123LGG G 2121LGG H3232LGGH(1)12312123212311 ()1LLLLGG HG G HGG G 11 1231111122123121232( )( )1 ()1GG GPPC sPR sLLLGG G

12、GG HG G HR(s)C(s)L1= G1 H1L2= G3 H3L3= G1G2G3H3H1L4= G4G3L5 = G1G2G3L1L2= (G1H1) (G3H3) = G1G3H1H3L1L4=(G1H1)(G4G3)=G1G3G4H1 G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s)

13、G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s)H3(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G1(s) G2(s) G3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s)G4(s)G3(s) H1(s)H3(s) G1(s) G2(s

14、) G4(s) H1(s)H3(s) G1(s) G2(s) G3(s)P2= G4G3P1=G1G2G31=12=1+G1H1C(s)R(s)=?请写出结果G1(s)G3(s)H1(s)G2(s)H3(s)H2(s)R(s)C(s)N(s)E(S)G1(s)G3(s)H1(s)G2(s)H3(s)H2(s)R(s)C(s)N(s)E(S)P1=11=1+G2H2P11= ?E(s)=1+ G2H2+ G1G2H3-G1H1G2 H2- G1H1(G2H3)R(s) N(s)(1+G2H2) (- G3G2H3)+R(s)E(S)G1(s)G3(s)H1(s)G2(s)H3(s)H2(s)C(s)N(s)R(s)E(S)G3(s)G2(s)H3(s)E(S)R(s)G1(s)H1(s)H2(s)C(s)P2= - G3G2H32= 1P22=?P1= G2H31= 1N(s)G1(s)H1